Does iPhone 17 Pro Max (ch) support FaceTime and AI?

Facetime Audio is not available on devices sold in China. Neither is Apple Intelligence.

Facetime Video is available on those devices.

Yes, the iPhone 17 Pro Max supports both FaceTime (Apple's video calling application) and Apple Intelligence.

The FaceTime app currently supports iPhones as old as the 5s, 6, and 6 Plus – three very old iPhones that cannot update past.

As for Apple Intelligence, the iPhone 17 Pro Max not only will support it, but will be one of a small group of phones which will receive enhancements to improve Dictation accuracy. (That feature requires 12 GB of RAM or more and the three models that will receive it are also the only three that have that much RAM.)

Apple Intelligence and Siri - Apple

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[EDIT: Note that Apple Intelligence may not be available in some countries and regions. If, when you said "part number ch", you were asking about models meant for the mainline China market, I do not think they have Apple Intelligence, due to Chinese government restrictions. Their hardware might be perfectly capable of running Apple Intelligence - but until such time as the Chinese government allowed them to receive it, they would not get the feature.

See the notes "For China Residents" in How to get Apple Intelligence - Apple Support .]

[EDIT 2: Some Web sites indicate that China disables some FaceTime features both on phones sold for other markets, and on phones sold for mainland China. E.g.., https://chinasurvivalkit.com/blog/does-facetime-work-in-china indicates that FaceTime audio calls will never work on an iPhone sold for the mainland China market … and that even for iPhones sold elsewhere, group FaceTime calls will not work as long as you are within the Great Firewall.]